The Buccaneers took the lead following a fumble by Cardinals running back Rashard Mendenhall. Rookie quarterback Mike Glennon's drove his team downfield and then hit receiver Mike Williams for a eight-yard strike in the end zone, the thrower's first in the NFL.
Both defenses tightened up as both Glennon and Cardinals quarterback Carson Palmer struggled to get into a rhythm to get their offenses moving downfield.
Just before the break, Glennon got into a groove finding Williams on a strike to move his side into field goal range and Rian Lindell put a 50-yard effort through the posts to extend his side's advantage to 10 points.
The Cardinals looked to get back into the game early in the third quarter as Palmer drove them downfield, but he threw an interception in the end zone as cornerback Johnathan Banks made a brilliant play to tip the ball up and catch it himself.
Defense again dominated in the third quarter as both teams struggled to get on the board at Raymond James Stadium.
The visitors finally secured three points in the game when Jay Feely hit a 42-yard field goal through the posts in the fourth quarter, leaving his side trailing by seven.
Cardinals quarterback Patrick Peterson intercepted Glennon late in the game inside the Buccaneers' own 20, which allowed his side to kick a field goal from the boot of Jay Feely from 27 yards out to give them the lead.
Bruce Arians's side sealed their comeback win as Peterson intercepted another Glennon pass, allowing Palmer to kneel out for the victory.